Mask design using library of corrections

ABSTRACT

Systems, techniques, and approaches to quickly generate mask patterns, synthesize near-fields, and design masks. In one aspect, a mask may be designed by modeling the transmitted field using a library of corrections and a fast field model.

This application is a continuation-in-part of and claims priority toU.S. application Ser. No. 10/789,703, filed Feb. 27, 2004 now U.S. Pat.No. 7,294,437.

BACKGROUND

Electronic devices, such as processors, may be formed by patterningsuccessive layers on a substrate using lithography. The patterns areformed using an imaging plate such as a mask or reticle that is designedto produce the desired features on the substrate. As device featuresizes decrease, more complex mask designs are used.

For example, masks incorporating phase shift technology (referred to asphase shift masks) may be used to pattern small features. In a non-phaseshift mask, the light transmitted through adjacent features is in phase,so that between adjacent features the amplitude of the light addstogether. In a phase shift mask, light transmitted through adjacentfeatures may be phase shifted so that between the features the amplitudeof the light from one feature is about equal to but opposite in sign tothe amplitude of the light from the other feature. This destructiveinterference may allow greater control over the creation of smallfeatures.

Mask design may be performed using software. For complex mask designs(e.g., design of phase shift masks for sub-wavelength features),accurate mask design software may be undesirably slow. In contrast,faster mask design software may not be suitably accurate.

A number of different methods may be used by the software to designmasks. For example, a method referred to as a thin mask method usesgeometrical optics to calculate the transmitted field, ignoring lightscattering effects due to mask features. A boundary layer methodmodifies the thin mask field in feature edge areas (the so-calledboundary layer) to account for some scattering effects. The edge domaindecomposition method adds edge scattering corrections to the thin maskfield to improve the accuracy.

DESCRIPTION OF DRAWINGS

FIG. 1 is a cross-sectional side view of an isolated edge in a mask anda plot of the transmitted field.

FIG. 2 is a flowchart illustrating a method to design a mask to quicklyand accurately generate desired features onto a substrate.

FIG. 3 illustrates one way to synthesize the near-field.

FIG. 4 is an embodiment of a system for creating a mask.

FIG. 5 is a cross-sectional side view of an isolated space in a mask anda plot of the transmitted field.

FIG. 6 is a flowchart for calculating an entry in the library ofcorrections.

FIG. 7 is an embodiment of a system to generate a library ofcorrections.

FIG. 8 is a flowchart illustrating a way to quickly calculate a mask.

FIG. 9 is a chart comparing computation times for two methods ofcalculating the near-field during mask design.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Systems and techniques described herein may allow for relativelyaccurate and fast mask design.

The first stage in mask design may involve identifying the desiredfeatures to be etched onto a substrate. The mask designer then creates amask that he thinks will produce these desired features. To model thefeatures that would result from applying the mask, the designer modelsthe pattern of the electromagnetic (EM) field transmitted through themask. Based on a comparison of the modeled features to the desiredfeatures, the designer may change his mask and repeat this process.

A key part of this process is the modeling of the transmitted EM field.A more accurate model of the EM field leads to a mask that moreaccurately produces the desired features.

Many rigorous methods exist to accurately determine the transmitted EMfield. For example, in the Finite Difference Time Domain method, theMaxwell equations are replaced by a set of finite difference equationsobtained by discretizing the Maxwell equations in space and time. Theyare essentially relationships between current states and the states ofthe next time step. The problem is then solved by marching the solutionsin time.

Another rigorous method, the Waveguide method, is a frequency domainmethod in which the simulation area is divided into 2D or 3D rectangularblocks. The material is considered uniform throughout each block so thatthe Maxwell equations can be solved analytically for each block.Solutions of all blocks are related by boundary conditions, which resultin a set of linear algebraic questions that are then solved using matrixmethods.

However, the computation time associated with applying these or otherrigorous methods to model transmitted EM field is prohibitive. Becauseof this difficulty, many mask designers employ a so-called “fastmethod.” For example, in the geometric optics method, the amplitude ofthe transmitted EM field in portions where the mask is chrome (or otherlight-blocking material) is considered to be zero. Where the mask isglass (or other light-passing material), the field is considered to beequivalent to the EM source. Although this method is simply and quicklycalculated, it ignores some of the physics of EM field transmission,such as diffusion around edges and interferences that may be caused bynearby features.

FIG. 1 illustrates this concept. The mask 100 is of an isolated edge 105that has a glass portion 110 and a light-blocking chrome portion 120. Inthe figure, light is transmitted through the mask in the direction shownby the arrow 130. Plot 140 shows the geometric optics model of thenear-field, and plot 150 illustrates a calculation of the near-fieldusing a rigorous method. A comparison of the two plots demonstrates thatthere is a certain amount of error associated with using a fast methodto determine the near-field. This error is indicated by the shadedportions 160. (Note that all the plots in the attached figures indicateamplitude only, not phase.)

Because fast methods only approximate the transmitted EM field, they mayresult in masks that do not accurately create the desired features. Arigorous model alternative, however, may allow accurate masks but themodel may be too computationally intensive for practical use. Thepresent approach offers a both fast and accurate way to model thetransmitted EM field and thereby to design an accurate mask.

The flowchart in FIG. 2 illustrates a method to design a mask to quicklyand accurately generate desired features onto a substrate. In block 210,the desired features are identified. Based on these features, a bestestimate mask is designed in block 220. A mask may consist of acombination of edges, corners, spaces, and other shapes; these shapesmay be referred to as primitives. In block 230, the mask isdeconstructed into its primitives. The corrections corresponding to theprimitives are retrieved from the corrections library in block 240.These corrections are used in block 250 to synthesize the near-field.This will be discussed in more detail below. In block 260, a simulationis conducted using the synthesized field to determine the features thatwould be generated by using the mask. The simulated features arecompared to the desired features in block 270 to determine whether thesimulated features are sufficiently similar to the desired features thatthe mask should be used without further modification. If so, the processends in block 280. If not, the mask is modified in block 290 to try togenerate features that are closer to the desired features. The processthen loops back to block 230 to analyze the modified mask.

FIG. 3 illustrates one way to accomplish the synthesis of block 250.First, the mask layout is used to construct a geometric field in block310. The edge corrections from the corrections library are added to thisgeometric field in block 320. Edge-to-edge corrections from the libraryare then added in block 330 and corner corrections are added in block340. The resulting synthesized field corresponds to the field that wouldresult from using a rigorous method. These corrections are discussed inmore detail below in connection with the creation of the library.

FIG. 4 shows a system for creating a mask according to an embodiment. Amask manipulator module 410 is coupled to a user input module 420, adisplay module 430, a mask deconstructor 440, an EM field synthesizer450, a feature calculator 460, a feature comparator 470, and a libraryof corrections for primitives 480.

An initial mask is input into the mask manipulator 410 and the maskdeconstructor 440 deconstructs the mask into its primitives (e.g.,edges, edge-to-edge interactions, corners, etc.). The EM fieldsynthesizer 450 looks up the correction for each primitive in thelibrary of corrections 480 and then applies these corrections to anappropriate fast method. The resulting synthesized field corresponds tothe field that would be calculated using a rigorous method. This isdiscussed in more detail below in connection with the creation of thelibrary.

The feature calculator 460 uses the synthesized field to determine thefeatures that would result from the application of the mask. The featurecomparator 470 then compares these features with the desired features.The mask manipulator 410 changes the mask to reduce the discrepancybetween the desired features and the synthesized features, and theresulting new mask is analyzed in the same way as described above.

The display 430 may show the synthesized field as well as the results ofthe comparison done by the feature comparator 470. If any user input isrequired, it may be given using the user input module 420.

Various tasks may be performed manually or automatically. For example,the feature comparator 470 may perform its comparison automatically orwith input from the user. A user may deconstruct a mask manually insteadof allowing the mask deconstructor 440 to do so automatically.Similarly, the mask manipulator 410 may make changes to a maskcompletely automatically or with some user interaction. (These aremerely non-exhaustive examples of tasks that may be performed withvarying degrees of automation.)

If there is no correction for a particular primitive on the mask in thelibrary, the correction for that primitive may be interpolated fromsimilar primitives. For example, suppose a mask has a space that is 25nm wide, but the closest corrections in the library are for spaces 20 nmand 30 nm wide. The correction for a 25 nm space may then be estimatedas, for example, a linear interpolation between the 20 nm correction andthe 30 nm correction. If the library contains primitives of sufficientnumber and variety, then interpolation may not introduce significanterror.

One important advantage of designing a mask as described above is thatvery small channels may be created. This results from the maskdesigner's ability to now quickly and accurately model the interactionbetween two edges that may be close together. Accordingly, in oneembodiment, channels may be designed and implemented that are of a widthequal to or less than the wavelength of the light being used.

In an embodiment, a simulated printed pattern generated for a maskdesign may be used to inspect a mask including the mask design. Masksmay also be generated using lithography techniques, and may acquiredefects during the manufacturing process or from contamination. The maskmay be inspected by comparing an actual printed pattern generated usingthe mask to the simulated printed pattern generated for the mask design.Any deviations between the simulated and actual printed patterns mayindicate a defect on the mask.

Creating a Library of Corrections

The library of corrections comprises entries that reflect the errorassociated with using a fast model instead of a rigorous method todetermine the transmitted EM field. For example, the shaded portions 160in FIG. 1 indicate the error associated with using a geometric modelinstead of a rigorous method to calculate the transmitted field for anisolated edge. This error may be calculated by subtracting the geometricmodel from the rigorous calculation. This quantity is called the “edgecorrection” because the addition of the quantity to the geometric model“corrects” it to conform to the rigorous model.

Similarly, an edge-to-edge interaction correction can be calculated.FIG. 5 represents an isolated pair of edges 505 and 507 in a mask 500.The mask has a light-transmitting portion 510 and a light-blockingportion 520. Light is directed into the mask in the direction shown byarrow 530. Plot 540 illustrates the geometric model of the amplitude ofthe transmitted field, and plot 550 represents the transmitted fieldcalculated using a rigorous method. The shaded portion 560 representsthe error associated with using the geometric model rather than arigorous method. To calculate an edge-to-edge interaction correction,the geometric field and the edge corrections are subtracted from therigorous field. The edge corrections are subtracted to isolate the errorassociated with the interaction of the edges. Reconstruction of therigorous field then involves adding both the edge corrections and theedge-to-edge interaction corrections to the geometric field.

Alternatively, a space correction may be calculated. In one embodiment,this involves subtracting only the geometric field from the rigorousfield. The resulting space correction is represented by the shadedregion 560. Reconstructing the rigorous field would then involve addingonly the space correction to the geometric field; no other edgecorrections would be required (for this isolated space). Such a spacecorrection may be used in place of separate edge corrections andedge-to-edge interaction corrections. In another embodiment, spacecorrections may be calculated as the sum of: (a) the average of the edgecorrections on each side of the space, and (b) the edge-to-edgeinteraction correction between the two edges. The space correction forthe space located beyond the edge at the end of a mask may be calculatedas one-half the edge correction for that edge.

To extend this further, a corner correction may be calculated bysubtracting the geometric field and the edge corrections of an isolatedcorner from the rigorous field of the isolated corner.

There are numerous shapes for which corrections may be calculated. Forexample, a particular square shape may be a shape for which it may beuseful to have a correction present in the library. A correction may becalculated that allows a quick and accurate synthesis of the rigorousfield.

Corrections more advanced than edge corrections, such as spacecorrections, corner corrections, and shape corrections, may account forscattering effects and interactions between mask features, which may beimportant for sub-wavelength features.

FIG. 6 shows a flowchart for calculating an entry in the library ofcorrections. Block 610 starts with a primitive shape, e.g., an isolatededge. The rigorous geometric fields are calculated in blocks 620 and630, respectively. In block 640, the geometric field is subtracted fromthe rigorous field. Block 650 involves checking whether there are anymore basic primitives than the primitive shape under consideration. Forexample, the edges surrounding a space are more basic primitives thanthe space itself. If there are such more basic primitives, thecorrections for those primitives are subtracted in block 670 from theresult of block 640; the result of block 670 is then entered into thelibrary in block 680 as the correction for the primitive shape underconsideration. If there were not any more basic primitives in block 650,the result of block 640 is entered into the library in block 660.

The correction for each primitive may vary depending on many differentparameters. Thus, each correction may be calculated for severaldifferent values of the various parameters. These parameters may beformulated into an index to aid in retrieving entries from the library.For example, corrections may be dependent on one or more of thefollowing: illumination wavelength; glass material refractive index andextinction coefficient; absorber material refractive index; extinctioncoefficient; stack thickness; and glass phase trench side wall profileand undercut. In addition, an edge library may be dependent onadditional parameters, such as light polarization; phase/chrome on theleft side of the edge; and phase/chrome on the right side of the edge.Similarly, an edge-to-edge interaction library may have additionaldependencies on: light polarization; width between the two edges;phase/chrome on the left; phase/chrome in the middle; and phase/chromeon the right. This idea may be extended for libraries for other shapes,such as corners, which may be dependent on one or more of the following:light polarization; lower left phase/chrome; upper left phase/chrome;lower right phase/chrome; and upper right phase/chrome.

Additional observations may allow some libraries to be created bymanipulating other libraries. For example, a particular primitive may bethe mirror image of a second primitive for which a library alreadyexists. In that case, a library for the first primitive may be generatedas a mirror image of the library for the second primitive. Similarly, aprimitive may be a 90-degree clockwise geometric rotation of anotherprimitive; an entirely new library may be created simply by rotatingclockwise an existing library. Thus, performing some operations, such asthe geometric operations of mirror image, rotation, etc., may allowlibraries of corrections to be generated without the need to fullycalculate each library from scratch. This may reduce the time requiredto generate the libraries.

By calculating a library of corrections, the long computation timeassociated with using rigorous methods may be performed before themask-design process has even begun. The rigorous field (synthesized byadding the appropriate corrections to a fast method) may then be usedduring the design process without the delay involved with calculatingthe rigorous field itself. Moreover, the one-time investment incomputation time to create the library of corrections may allow for theunlimited use of those corrections to synthesize the rigorous field inthe design of future masks. Thus, once a rigorous method is used toconstruct the library, calculating the transmitted EM field is simply amatter of choosing the correct corrections from the library and applyingthese corrections to a fast method. The fast method used in synthesizingthe field using the corrections may be the same fast method that wasused in creating the corrections.

FIG. 7 shows an embodiment of a system to generate a library ofcorrections. A library generator module 710 is coupled to a user inputmodule 720, a display module 730, a parameters database 740, a rigorousfield generator 750, a fast field generator 760, a primitives database770, and a library of corrections for primitives 780.

The library generator 710 selects a primitive from the primitivesdatabase 770 and a set of parameters from the parameters database 740.These are used by the rigorous field generator 750 to generate a modelof the transmitted field using a rigorous method. Likewise, the fastfield generator 760 may use the same quantities to generate a model forthe transmitted field using a fast method, such as the geometric opticsmethod. The library generator 710 then subtracts the fast field from therigorous field. Additionally, if there are any corrections for morebasic primitives in the library 780, the library generator alsosubtracts those corrections from the rigorous field. The resultingcorrection is stored as an entry in the library 780. This entry may beindexed according to the values that were used from the parametersdatabase 740 and the primitives database 770.

In some implementations, the pattern in the mask includes pixels. Eachpixel may represent light-blocking or light-passing areas of the mask. Apixel may also represent a phase-shifting area of the mask. Each ofthese pixels may be treated as primitives, or several pixels may betreated together as a single primitive. For example, a vertical line oflight-passing pixels may represent a channel or a space in the mask. Insuch masks, mask design may be accomplished by changing thecharacteristics of one or more pixels in the mask and then re-analyzingthe mask.

A method may include receiving a first primitive shape, determining arigorous field corresponding to the first primitive shape, determining ageometric field corresponding to the first primitive shape, andcalculating a first correction by subtracting the geometric field fromthe rigorous field. A method may also include checking whether a secondprimitive shape is more basic than the first primitive shape, if thesecond primitive shape is more basic than the first primitive shape,calculating a library entry for the first primitive shape by subtractinga second correction for the second primitive shape from the firstcorrection, and if the second primitive shape is not more basic than thefirst primitive shape, entering the first correction as a library entryfor the first primitive shape.

A method for synthesizing a near-field may include constructing ageometric field from a mask layout, applying an edge correction,applying an edge-to-edge interaction correction, and applying a cornercorrection.

A method may include selecting a primitive from a primitives database,selecting a set of parameters from a parameters database, using theprimitive and the set of parameters to generate a rigorous model of atransmitted field using a rigorous method, using the primitive and theset of parameters to generate a fast model for the transmitted fieldusing a fast method, generating a correction, comprising subtracting thefast model from the rigorous model, and storing the correction in alibrary.

An apparatus may include a primitives database, a parameters database, arigorous field generator for generating a rigorous field model of atransmitted field using a rigorous method, a fast field generator forgenerating a fast field model for the transmitted field using a fastmethod, and a library generator for generating a correction bysubtracting from the rigorous field model the fast field model andfurther subtracting all corrections for any more basic primitives in alibrary.

A method may include: (a) receiving a first mask pattern, with at leasta portion of the first mask pattern having a first mask feature; (b)synthesizing a first near-field corresponding to the at least a portionof the first mask pattern using a library of corrections; (c) generatinga second mask pattern by modifying the first mask pattern, with themodifying the first mask pattern including modifying the first maskfeature; (d) determining a first effect on the first near-fieldcorresponding to the modifying the first mask feature; (e) synthesizinga second near-field corresponding to at least a portion of the secondmask pattern by applying the first effect to the first near-field; (f)using the second near-field to determine a second wafer patterncorresponding to the at least a portion of the second mask pattern; and(g) comparing the second wafer pattern to a desired wafer pattern.

A mask may be designed by (a) receiving a first mask pattern, with atleast a portion of the first mask pattern having a first mask feature;(b) synthesizing a first near-field corresponding to the at least aportion of the first mask pattern using a library of corrections; (c)generating a second mask pattern by modifying the first mask pattern,with the modifying the first mask pattern including modifying the firstmask feature; (d) determining a first effect on the first near-fieldcorresponding to the modifying the first mask feature; (e) synthesizinga second near-field corresponding to at least a portion of the secondmask pattern by applying the first effect to the first near-field; (f)using the second near-field to determine a second wafer patterncorresponding to the at least a portion of the second mask pattern; and(g) comparing the second wafer pattern to a desired wafer pattern.

A processor may be designed using a mask that may have been designed by:(a) receiving a first mask pattern, with at least a portion of the firstmask pattern having a first mask feature; (b) synthesizing a firstnear-field corresponding to the at least a portion of the first maskpattern using a library of corrections; (c) generating a second maskpattern by modifying the first mask pattern, with the modifying thefirst mask pattern including modifying the first mask feature; (d)determining a first effect on the first near-field corresponding to themodifying the first mask feature; (e) synthesizing a second near-fieldcorresponding to at least a portion of the second mask pattern byapplying the first effect to the first near-field; (f) using the secondnear-field to determine a second wafer pattern corresponding to the atleast a portion of the second mask pattern; and (g) comparing the secondwafer pattern to a desired wafer pattern.

An article may include a machine-readable medium that includesmachine-executable instructions that are operative to cause one or moremachines to perform operations such as those described above andelsewhere herein. Thus, an article may include a machine-readable mediumthat includes machine-executable instructions that are operative tocause one or more machines to: (a) receive a first mask pattern, atleast a portion of the first mask pattern having a first mask feature;(b) synthesize a first near-field corresponding to the at least aportion of the first mask pattern using a library of corrections; (c)generate a second mask pattern by modifying the first mask pattern, themodifying the first mask pattern comprising modifying the first maskfeature; (d) determine a first effect on the first near-fieldcorresponding to the modifying the first mask feature; (e) synthesize asecond near-field corresponding to at least a portion of the second maskpattern by applying the first effect to the first near-field; (f) usethe second near-field to determine a second wafer pattern correspondingto the at least a portion of the second mask pattern; and (g) comparethe second wafer pattern to a desired wafer pattern.

An apparatus may include a mask manipulator configured to change one ormore elements of a mask pattern and an electromagnetic field synthesizerthat is configured to identify the changed elements of the mask pattern,calculate the effects on a first near-field of the changed elements, andapply the effects to the first near-field to generate a secondnear-field.

FIG. 8 illustrates a quick mask design process. At block 810, an initialmask layout is created and the resulting near-field is synthesized. Atblock 820, one or more elements of the mask may be changed. This mayinvolve changing one or more pixels of the mask. Any changes made inblock 820 may be analyzed at block 830 to identify which elements of themask were added or removed. Elements that were modified but notcompletely deleted may be considered to have been removed and replacedwith a new element with modified characteristics.

At block 840, the effects of these mask elements on the near-field iscalculated. This may be done using a library of primitives. At block850, a new near-field may be synthesized by adding to thepreviously-synthesized near-field the effects of the new mask elementsand by subtracting from the previously-synthesized near-field theeffects of the removed mask elements.

The newly-synthesized near-field is used to run a simulation at block860 to determine the wafer features that would be generated by using themask. At block 870, the simulated features are compared to the desiredwafer pattern to determine whether the simulated features aresufficiently similar to the desired pattern that the mask should be usedwithout further modification. If so, the process ends in block 880. Ifnot, the process loops back to block 820 to modify the mask to try togenerate features that are closer to the desired wafer pattern.

FIG. 9 illustrates comparative computation times for synthesis of thenear-field for each iteration during iterative mask design as a functionof the area of the mask in square microns. Plot 910 corresponds to thecomputation time in which the near-field for the entire mask isrecalculated in each iteration, e.g., as in FIG. 2. Plot 920 correspondsto the computation time in which only the portion of the near-field thatwas different from the previously synthesized near-field is calculatedin each iteration, e.g., as in FIG. 8. As FIG. 9 shows, the computationtime associated with plot 910 increases as the mask area increases,whereas the computation time associated with plot 920 remainsessentially constant. For masks larger than 15 μm², calculating thenear-field for only the modified portions of the mask in each iterationof the mask design loop may provide more than a thousand-fold increasein mask design speed.

The system for designing a mask depicted in FIG. 4 may be used toimplement a quick mask design method. For example, the EM fieldsynthesizer 450 may implement the functionality of blocks 830, 840, and850 of FIG. 8.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made without departingfrom the spirit and scope of the invention. For example, the library isnot limited in the types of corrections present; it should be evidentthat there are many other types of corrections that may be in thelibrary (e.g. space corrections, corner-to-corner interactioncorrections, etc.). Also, blocks in a flowchart and various operationsdescribed above may be skipped or performed out of order and stillprovide desirable results. Various tasks may be performed automaticallyor manually. Accordingly, other implementations are within the scope ofthe following claims.

1. A method comprising: receiving a first mask pattern in a maskmanipulator module, at least a portion of the first mask pattern havinga first mask feature; synthesizing, in an electromagnetic fieldsynthesizer, a first near-field corresponding to said at least a portionof the first mask pattern using a library of corrections; generating, inthe mask manipulator module, a second mask pattern by modifying thefirst mask pattern, said modifying the first mask pattern comprisingmodifying the first mask feature; determining, in the electromagneticfield synthesizer, a first effect on the first near-field correspondingto said modifying the first mask feature; synthesizing, in theelectromagnetic field synthesizer, a second near-field corresponding toat least a portion of the second mask pattern by applying the firsteffect to the first near-field; using said second near-field todetermine a second wafer pattern corresponding to said at least aportion of the second mask pattern; and comparing, in a featurecomparator, the second wafer pattern to a desired wafer pattern.
 2. Themethod of claim 1, wherein said modifying the first mask featurecomprises removing the first mask feature.
 3. The method of claim 2,wherein said applying the first effect comprises subtracting the firsteffect from the first near-field.
 4. The method of claim 1, wherein saidmodifying the first mask feature comprises replacing the first maskfeature in the first mask with a different mask feature.
 5. The methodof claim 4, wherein said applying the first effect comprises:determining a removal effect on the first-near field corresponding to aremoval of the first mask feature from the first mask; determining anaddition effect on the first-near field corresponding to an addition ofthe different mask feature; subtracting the removal effect from thefirst near-field; and adding the addition effect to the firstnear-field.
 6. The method of claim 1, wherein said modifying the firstmask pattern comprises adding a new mask feature.
 7. The method of claim6, wherein said applying the first effect comprises adding the firsteffect to the first near-field.
 8. The method of claim 1, wherein saiddetermining the first effect on the first near-field comprisesretrieving a first correction from a library of corrections.
 9. Themethod of claim 1, wherein the first mask pattern, the second maskpattern, and the first mask feature each comprise a plurality of pixels.10. The method of claim 1, wherein the first mask pattern and the secondmask pattern each comprise a plurality of pixels, and wherein the firstmask feature consists essentially of one pixel.
 11. A mask comprising aspecific mask pattern, the specific mask pattern having been designedby: receiving a first mask pattern, at least a portion of the first maskpattern having a first mask feature; synthesizing a first near-fieldcorresponding to said at least a portion of the first mask pattern usinga library of corrections; generating a second mask pattern by modifyingthe first mask pattern, said modifying the first mask pattern comprisingmodifying the first mask feature; determining a first effect on thefirst near-field corresponding to said modifying the first mask feature;synthesizing a second near-field corresponding to at least a portion ofthe second mask pattern by applying the first effect to the firstnear-field; using said second near-field to determine a second waferpattern corresponding to said at least a portion of the second maskpattern; and comparing the second wafer pattern to a desired waferpattern.
 12. The mask of claim 11, wherein: (a) said modifying the firstmask feature comprises replacing the first mask feature in the firstmask with a different mask feature; and (b) said applying the firsteffect comprises: (1) determining a removal effect on the first-nearfield corresponding to a removal of the first mask feature from thefirst mask; (2) determining an addition effect on the first-near fieldcorresponding to an addition of the different mask feature; (3)subtracting the removal effect from the first near-field; and (4) addingthe addition effect to the first near-field.
 13. A processor having beendesigned using the mask of claim
 12. 14. A processor having beendesigned using the mask of claim
 11. 15. An article comprising amachine-readable medium including machine-executable instructions, theinstructions operative to cause one or more machines to: receive a firstmask pattern, at least a portion of the first mask pattern having afirst mask feature; synthesize a first near-field corresponding to saidat least a portion of the first mask pattern using a library ofcorrections; generate a second mask pattern by modifying the first maskpattern, said modifying the first mask pattern comprising modifying thefirst mask feature; determine a first effect on the first near-fieldcorresponding to said modifying the first mask feature; synthesize asecond near-field corresponding to at least a portion of the second maskpattern by applying the first effect to the first near-field; use saidsecond near-field to determine a second wafer pattern corresponding tosaid at least a portion of the second mask pattern; and compare thesecond wafer pattern to a desired wafer pattern.
 16. The article ofclaim 15, wherein said modifying the first mask feature comprisesremoving the first mask feature.
 17. The article of claim 16, whereinsaid applying the first effect comprises subtracting the first effectfrom the first near-field.
 18. The article of claim 15, wherein saidmodifying the first mask feature comprises replacing the first maskfeature in the first mask with a different mask feature.
 19. The articleof claim 18, wherein said applying the first effect comprises:determining a removal effect on the first-near field corresponding to aremoval of the first mask feature from the first mask; determining anaddition effect on the first-near field corresponding to an addition ofthe different mask feature; subtracting the removal effect from thefirst near-field; and adding the addition effect to the firstnear-field.
 20. The article of claim 15, wherein said modifying thefirst mask pattern comprises adding a new mask feature.
 21. The articleof claim 20, wherein said applying the first effect comprises adding thefirst effect to the first near-field.
 22. The article of claim 15,wherein the instructions operative to cause the one or more machines todetermine the first effect on the first near-field comprise instructionsoperative to cause the one or machines to retrieve a first correctionfrom a library of corrections.
 23. The article of claim 15, wherein thedesired wafer pattern includes a plurality of desired features, saiddesired features including features smaller than a wavelength of lightwith which a mask corresponding to the desired wafer pattern is to beilluminated.